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A305175 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 2, 3, 4, 6 or 7 king-move adjacent elements, with upper left element zero. 7
0, 0, 0, 0, 3, 0, 0, 5, 5, 0, 0, 18, 4, 18, 0, 0, 61, 46, 46, 61, 0, 0, 209, 151, 410, 151, 209, 0, 0, 702, 543, 2397, 2397, 543, 702, 0, 0, 2381, 2120, 13970, 26810, 13970, 2120, 2381, 0, 0, 8069, 8155, 93426, 218476, 218476, 93426, 8155, 8069, 0, 0, 27330, 30205, 586718 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,5
COMMENTS
Table starts
.0....0.....0.......0.........0..........0............0..............0
.0....3.....5......18........61........209..........702...........2381
.0....5.....4......46.......151........543.........2120...........8155
.0...18....46.....410......2397......13970........93426.........586718
.0...61...151....2397.....26810.....218476......2416954.......24233688
.0..209...543...13970....218476....2549718.....40793823......587542013
.0..702..2120...93426...2416954...40793823...1069089450....24206013485
.0.2381..8155..586718..24233688..587542013..24206013485...830801270567
.0.8069.30205.3677924.237639509.8317497391.531063626743.27606232235363
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 3*a(n-1) +a(n-2) +2*a(n-3) -2*a(n-4) -4*a(n-5) for n>6
k=3: [order 18]
k=4: [order 66] for n>67
EXAMPLE
Some solutions for n=5 k=4
..0..1..0..1. .0..0..1..0. .0..1..0..1. .0..0..1..0. .0..1..0..1
..0..1..0..0. .1..1..1..1. .1..1..0..0. .1..1..1..1. .1..0..1..0
..0..0..0..1. .1..1..1..0. .0..1..1..1. .0..1..0..1. .0..0..0..0
..0..1..0..1. .0..0..1..0. .0..1..0..1. .0..0..1..0. .1..0..1..1
..1..0..1..0. .1..1..1..0. .0..1..1..0. .1..1..0..1. .0..1..0..0
CROSSREFS
Column 2 is A303684.
Sequence in context: A303690 A304156 A305509 * A316763 A304065 A305457
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, May 26 2018
STATUS
approved

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Last modified July 14 16:06 EDT 2024. Contains 374322 sequences. (Running on oeis4.)